with \(T_i(s_i,{x}_i)=f_i({x}_i)+\frac{1}{2}s_i \rho _i({x}_i(t))\) . Motivated by [1]}, let \(\lbrace p_i,v_i\rbrace  \in \Omega _{x_i}\)  be a compact set, then \(\Omega _{\varphi _i} \subset \Omega _{x_i}\) , where \(\Omega _{\varphi _i} = \lbrace s_i \ | \ ||s_i|| < o_i \rbrace \)  with \(o_i\)  chosen as a small arbitrary constant. As \(\Omega _{\varphi _i}\)  is an open set, its complement set, \(\Omega ^0_{\varphi _i} =\Omega _{x_i}-\Omega _{\varphi _i}\) , is a compact set.
